
#. 1) The higher the correlation, the more shared information there is. So, the probabilities of the
#.    second hidden state are more dependent on the first (and vice versa).

#. 2) The means control only the location! The variances determine the spread in X and Y. The
#.    correlation is the only factor that controls the degree of the 'rotation', where we can think
#.    about the correlation as forcing the distribution to be more along one of the diagonals or ther
#.    other.

#. 3) We would need to marginalize! We will do this next.